The Multi-Maximum and Quasi-Maximum Common Subgraph Problem

The Maximum Common Subgraph problem has been long proven NP-hard. Nevertheless, it countless practical applications, and researchers are still searching for exact solutions scalable heuristic approaches. Driven by applications in molecular science cyber-security, we concentrate on the among an indefinite number of graphs. We first extend a state-of-the-art branch-and-bound procedure working two graphs to N Then, given high computational cost this approach, trade off complexity accuracy, propose set heuristics approximate solution analyze sequential, parallel multi-core, parallel-many core (GPU-based) approaches, exploiting several leveraging techniques decrease contention threads, improve workload balance different tasks, reduce computation time, increase final result size. also present sorting order vertices themselves. compare our algorithms with method publicly available benchmark sets. On graph pairs, able speed up 2× factor, pruning search space more than 60%. sets graphs, all extremely time-consuming complex application many real cases. contrary, far less expensive (as they show lower-bound 10×), have better asymptotic (with ups orders magnitude experiments), obtain excellent approximations maximal 98.5% nodes average.